On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.

The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside C_c (where C_c is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within C_c.-Author